30 citations · 193 across the 29 of their papers we have counts for
9 papers · 1 filter
Orthogonality with Respect to the Hermite Product, KP Wave Functions, and the Bispectral Involution
Alex Kasman, Rob Milson, Michael Gekhtman
It is well known that for any wave function of the KP hierarchy, there is another wave function called its ''adjoint'' such that the path integral of their product with re…
Inverse moment problem for non-Abelian Coxeter double Bruhat cells
Michael Gekhtman
We solve the inverse problem for non-Abelian Coxeter double Bruhat cells in terms of the matrix Weyl functions. This result can be used to establish complete integrability of the n…
Strong asymptotics for Cauchy biorthogonal polynomials with application to the Cauchy two--matrix model
Marco Bertola, Michael Gekhtman, Jacek Szmigielski
We apply the nonlinear steepest descent method to a class of 3x3 Riemann-Hilbert problems introduced in connection with the Cauchy two-matrix random model. The general case of two…
Spin Calogero Particles and Bispectral Solutions of the Matrix KP Hierarchy
Maarten Bergvelt, Michael Gekhtman, Alex Kasman
Pairs of matrices whose commutator differ from the identity by a matrix of rank are used to construct bispectral differential operators with matrix coef…
Multi-Hamiltonian structure for the finite defocusing Ablowitz-Ladik equation
Michael Gekhtman, Irina Nenciu
We study the Poisson structure associated to the defocusing Ablowitz-Ladik equation from a functional-analytical point of view, by reexpressing the Poisson bracket in terms of the…
Biorthogonal Laurent polynomials, Toeplitz determinants, minimal Toda orbits and isomonodromic tau functions
M. Bertola, M. Gekhtman
We consider the class of biorthogonal polynomials that are used to solve the inverse spectral problem associated to elementary co-adjoint orbits of the Borel group of upper triangu…
Inverse moment problem for elementary co-adjoint orbits
L. Faybusovich, M. Gekhtman
We give a solution to the inverse moment problem for a certain class of Hessenberg and symmetric matrices related to integrable lattices of Toda type.
Poisson brackets on rational functions and multi-Hamiltonian structure for integrable lattices
L. Faybusovich, M. Gekhtman
We introduce a family of compatible Poisson brackets on the space of rational functions with denominator of a fixed degree and use it to derive a multi-Hamiltonian structure for a…
On billiard weak solutions of nonlinear PDE's and Toda flows
Mark Alber, Roberto Camassa, Michael Gekhtman
A certain class of partial differential equations possesses singular solutions having discontinuous first derivatives ("peakons"). The time evolution of peaks of such solutions is…